where <code>(tx,ty,tz)</code> is a translation vector, <code>(sx,sy,sz)</code> is a scaling vector and <code>(rx,ry,rz)</code> is a rotation vector (angles in degrees around each principal direction). Note that the translation is always performed after rotation and scaling.

where <code>(tx,ty,tz)</code> is a translation vector, <code>(sx,sy,sz)</code> is a scaling vector and <code>(rx,ry,rz)</code> is a rotation vector (angles in degrees around each principal direction). Note that the translation is always performed after rotation and scaling.

-

If the <code>scale</code> parameter is specified, uniform scaling is applied along the three axis.

+

If the <code>scale</code> parameter is specified, uniform scaling is applied along the three axes.

The <code>flip</code> parameter can be used to flip the surface orientation.

The <code>flip</code> parameter can be used to flip the surface orientation.

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;Difference: A - B = { <code>MAX (fA(x,y,z), - fB(x,y,z))</code> }

;Difference: A - B = { <code>MAX (fA(x,y,z), - fB(x,y,z))</code> }

-

For example the following will replicate the [[:w:Image:Csg tree.png|example]] of the wikipedia [[:w:Constructive solid geometry|CSG]] page

+

Three predefined macros can be used to perform these boolean operations. For example the following will replicate the [[:w:Image:Csg tree.png|example]] of the wikipedia [[:w:Constructive solid geometry|CSG]] page

Solid ({

Solid ({

double s = sphere (0, 0, 0, 0.25);

double s = sphere (0, 0, 0, 0.25);

double c = cube (0,0,0,0.38);

double c = cube (0,0,0,0.38);

-

double sIc = MAX (s, c);

+

double sIc = intersection (s, c);

double cylinder1 = x*x + y*y - 0.12*0.12;

double cylinder1 = x*x + y*y - 0.12*0.12;

double cylinder2 = z*z + y*y - 0.12*0.12;

double cylinder2 = z*z + y*y - 0.12*0.12;

double cylinder3 = x*x + z*z - 0.12*0.12;

double cylinder3 = x*x + z*z - 0.12*0.12;

-

double cylinderU = MIN (MIN (cylinder1, cylinder2), cylinder3);

+

double cylinderU = union (union (cylinder1, cylinder2), cylinder3);

-

return MAX (sIc, - cylinderU);

+

return difference (sIc, cylinderU);

})

})

Current revision

A GfsSurface is an oriented surface (in 3D) or an oriented curve (in 2D).

The surface can be defined implicitly using for example:

(x*x + y*y + z*z - 0.1*0.1)

which defines the surface as the set of points of coordinates (x,y,z) such that x*x + y*y + z*z - 0.1*0.1 = 0 (i.e. a sphere of radius 0.1 centered on the origin).

The sign of the implicit function defines the surface orientation. The function should be continuous. For example it is not a good idea to do

where (tx,ty,tz) is a translation vector, (sx,sy,sz) is a scaling vector and (rx,ry,rz) is a rotation vector (angles in degrees around each principal direction). Note that the translation is always performed after rotation and scaling.

If the scale parameter is specified, uniform scaling is applied along the three axes.

The flip parameter can be used to flip the surface orientation.

If set to one the twod parameter "flattens" the surface on the z = 0 plane (this is used in 3D by the GfsRefineSurface object).

Several simple implicit surfaces are pre-defined:

ellipse(x,y,a,b)

an ellipse (an elliptical prism in 3D) centered on (x,y) and with semimajor axis a and semiminor axis b.

Boolean operations

Boolean operations between implicit surfaces can be used to create more complex objects (a technique also know as Constructive Solid Geometry). Given two implicit surfaces A and B with associated implicit functions fA and fB, the standard boolean set operations can be constructed as:

Intersection

A ^ B = { MAX (fA(x,y,z), fB(x,y,z)) }

Union

A U B = { MIN (fA(x,y,z), fB(x,y,z)) }

Difference

A - B = { MAX (fA(x,y,z), - fB(x,y,z)) }

Three predefined macros can be used to perform these boolean operations. For example the following will replicate the example of the wikipedia CSG page